Apr 23, 2014 · A good way to visualize them is to construct a triangle whose angles are $\frac {\pi} {a}$, $\frac {\pi} {b}$, and $\frac {\pi} {c}$, and then to reflect that triangle across each of its …

Mar 19, 2019 · While that matrix could belong to a matrix group that represents the symmetry group of an equilateral triangle, some limitations on coordinates for the triangle coordinates will …

Apr 4, 2020 · How is this done? Treating the integers as mod 7 7 will obviously create a finite group (which is apparently isomorphic to the (2, 3, 7) (2, 3, 7) triangle group, but on the Klein …

Sep 7, 2017 · This shows that the symmetry of an equilateral triangle is abstractly the same as the permutations of the numbers 1, 2, and 3, and the two situations can be studied at the same time.

Apr 13, 2017 · This answer made me wonder if there is a geometrical way to prove that the triangle group $ (\alpha,\alpha,\alpha)$ is a subgroup of the triangle group $ (3,3,\alpha)$.

Jul 2, 2024 · I want to find all quotients of ordinary hyperbolic triangle group (2,3,8). In general the "Triangle type" indicates the three positive integers p, q and r in the defining …

Feb 23, 2022 · @StevenStadnicki Yes, $\Gamma$ should be isomorphic to the fundamental group of a genus-3 surface. 336 is the number of Schwarz triangles in Klein's "Hauptfigur" …

Nov 30, 2022 · The group acts on the triangle. That means that it acts on the set of possible ways to color the triangle. It doesn't act on the colors, it acts on the triangle, or it acts on the set of …

Sep 2, 2020 · The answer for hyperbolic triangle groups is: No. Every hyperbolic triangle group $\Delta (p, q, r)$ has finite quotient groups which are not isomorphic to subgroup of $\Delta (p, …

Aug 26, 2022 · I am an undergraduate student looking into the quotients of hyperbolic space by triangle groups. For clarity, a triangle group is a group generated by reflections in the sides of …